arXiv subjects

Steven R. White

Publications and source records attributed to Steven R. White.

At least 55 records · Page 3Linked to original sources

arXiv2020

Ground-state properties of the hydrogen chain: insulator-to-metal transition, dimerization, and magnetic phases

Accurate and predictive computations of the quantum-mechanical behavior of many interacting electrons in realistic atomic environments are critical for the theoretical design of materials with desired properties, and require solving the grand-challenge problem of the many-electron Schrodinger equation. An infinite chain of equispaced hydrogen atoms is perhaps the simplest realistic model for a bulk material, embodying several central themes of modern condensed matter physics and chemistry, while retaining a connection to the paradigmatic Hubbard model. Here we report a combined application of cutting-edge computational methods to determine the properties of the hydrogen chain in its quantum-mechanical ground state. Varying the separation between the nuclei leads to a rich phase diagram, including a Mott phase with quasi long-range antiferromagnetic order, electron density dimerization with power-law correlations, an insulator-to-metal transition and an intricate set of intertwined magnetic orders.

cond-mat.str-el↗

arXiv2020

Critical properties of a comb lattice

In this paper we study the critical properties of the Heisenberg spin-1/2 model on a comb lattice -- a 1D backbone decorated with finite 1D chains -- the teeth. We address the problem numerically by a comb tensor network that duplicates the geometry of a lattice. We observe a fundamental difference between the states on a comb with even and odd number of sites per tooth, which resembles an even-odd effect in spin-1/2 ladders. The comb with odd teeth is always critical, not only along the teeth, but also along the backbone, which leads to a competition between two critical regimes in orthogonal directions. In addition, we show that in a weak-backbone limit the excitation energy scales as $1/(NL)$, and not as $1/N$ or $1/L$ typical for 1D systems. For even teeth in the weak backbone limit the system corresponds to a collection of decoupled critical chains of length $L$, while in the strong backbone limit, one spin from each tooth forms the backbone, so the effective length of a critical tooth is one site shorter, $L-1$. Surprisingly, these two regimes are connected via a state where a critical chain spans over two nearest neighbor teeth, with an effective length $2L$.

cond-mat.str-el↗

arXiv2020

Plaquette versus ordinary $d$-wave pairing in the $t'$-Hubbard model on a width 4 cylinder

The Hubbard model and its extensions are important microscopic models for understanding high- $T_c$ superconductivity in cuprates. In the model with next-nearest-neighbor hopping $t'$ (the $t'$- Hubbard model), pairing is strongly influenced by $t'$ . In particular, a recent study on a width-4 cylinder observed quasi-long-rage superconducting order, associated with a negative $t'$ , which was taken to imply superconductivity in the two-dimensional (2D) limit. In this work we study more carefully pairing in the width-4 $t'$-Hubbard model. We show that in this specific system, the pairing symmetry with $t'<0$ is not the ordinary $d$-wave one would expect in the 2D limit. Instead we observe a so-called plaquette d-wave pairing. The plaquette d-wave exists only on a width-4 cylinder, and so is not representative of the 2D limit. We find that a negative $t'$ suppresses the conventional d-wave, leading to plaquette pairing. In contrast, a different $t''$ coupling acting diagonally on the plaquettes suppresses plaquette pairing, leading to conventional $d$-wave pairing.

cond-mat.str-el↗

arXiv2019

Discontinuous Galerkin discretization for quantum simulation of chemistry

Methods for electronic structure based on Gaussian and molecular orbital discretizations offer a well established, compact representation that forms much of the foundation of correlated quantum chemistry calculations on both classical and quantum computers. Despite their ability to describe essential physics with relatively few basis functions, these representations can suffer from a quartic growth of the number of integrals. Recent results have shown that, for some quantum and classical algorithms, moving to representations with diagonal two-body operators can result in dramatically lower asymptotic costs, even if the number of functions required increases significantly. We introduce a way to interpolate between the two regimes in a systematic and controllable manner, such that the number of functions is minimized while maintaining a block diagonal structure of the two-body operator and desirable properties of an original, primitive basis. Techniques are analyzed for leveraging the structure of this new representation on quantum computers. Empirical results for hydrogen chains suggest a scaling improvement from $O(N^{4.5})$ in molecular orbital representations to $O(N^{2.6})$ in our representation for quantum evolution in a fault-tolerant setting, and exhibit a constant factor crossover at 15 to 20 atoms. Moreover, we test these methods using modern density matrix renormalization group methods classically, and achieve excellent accuracy with respect to the complete basis set limit with a speedup of 1-2 orders of magnitude with respect to using the primitive or Gaussian basis sets alone. These results suggest our representation provides significant cost reductions while maintaining accuracy relative to molecular orbital or strictly diagonal approaches for modest-sized systems in both classical and quantum computation for correlated systems.

quant-ph↗

arXiv2019

Comb tensor networks

In this paper we propose a special type of a tree tensor network that has the geometry of a comb---a 1D backbone with finite 1D teeth projecting out from it. This tensor network is designed to provide an effective description of higher dimensional objects with special limited interactions, or, alternatively, one-dimensional systems composed of complicated zero-dimensional objects. We provide details on the best numerical procedures for the proposed network, including an algorithm for variational optimization of the wave-function as a comb tensor network, and the transformation of the comb into a matrix product state. We compare the complexity of using a comb versus alternative matrix product state representations using density matrix renormalization group (DMRG) algorithms. As an application, we study a spin-1 Heisenberg model system which has a comb geometry. In the case where the ends of the teeth are terminated by spin-1/2 spins, we find that Haldane edge states of the teeth along the backbone form a critical spin-1/2 chain, whose properties can be tuned by the coupling constant along the backbone. By adding next-nearest-neighbor interactions along the backbone, the comb can be brought into a gapped phase with a long-range dimerization along the backbone. The critical and dimerized phases are separated by a Kosterlitz-Thouless phase transition, the presence of which we confirm numerically. Finally, we show that when the teeth contain an odd number of spins and are not terminated by spin-1/2's, a special type of comb edge states emerge.

cond-mat.str-el↗

arXiv2018

Multi-sliced Gausslet Basis Sets for Electronic Structure

We introduce highly local basis sets for electronic structure which are very efficient for correlation calculations near the complete basis set limit. Our approach is based on gausslets, recently introduced wavelet-like smooth orthogonal functions. We adapt the gausslets to particular systems using one dimensional coordinate transformations, putting more basis functions near nuclei, while maintaining orthogonality. Three dimensional basis functions are composed out of products of the 1D functions in an efficient way called multislicing. We demonstrate the new bases with both Hartree Fock and density matrix renormalization group (DMRG) calculations on hydrogen chain systems. With both methods, we can go to higher accuracy in the complete basis set limit than is practical for conventional Gaussian basis sets, with errors near 0.1 mH per atom.

physics.chem-ph↗

arXiv2018

The t-t'-J model in one dimension using extremely correlated Fermi liquid theory and time dependent density matrix renormalization group

We study the one dimensional t-t'-J model for generic couplings using two complementary theories, the extremely correlated Fermi liquid theory and time-dependent density matrix renormalization group over a broad energy scale. The two methods provide a unique insight into the strong momentum dependence of the self-energy of this prototypical non-Fermi liquid, described at low energies as a Tomonaga-Luttinger liquid. We also demonstrate its intimate relationship to spin-charge separation, i.e. the splitting of Landau quasiparticles of higher dimensions into two constituents, driven by strong quantum fluctuations inherent in one dimension. The momentum distribution function, the spectral function, and the excitation dispersion of these two methods also compare well.

cond-mat.str-el↗

arXiv2018

Topography of Spin Liquids on a Triangular Lattice

Spin systems with frustrated anisotropic interactions are of significant interest due to possible exotic ground states. We have explored their phase diagram on a nearest-neighbor triangular lattice using the density-matrix renormalization group and mapped out the topography of the region that can harbor a spin liquid. We find that this spin-liquid phase is continuously connected to a previously discovered spin-liquid phase of the isotropic $J_1\!-\!J_2$ model. The two limits show nearly identical spin correlations, making the case that their respective spin liquids are isomorphic to each other.

cond-mat.str-el↗

arXiv2018

Chemical accuracy from small, system-adapted basis functions

We propose a general method for constructing system-dependent basis functions for correlated quantum chemical calculations. Our construction combines features from several traditional approaches: plane waves, localized basis functions, and wavelets. In a one-dimensional mimic of Coulomb systems, it requires only 2-3 basis functions per electron to achieve chemical accuracy, and reproduces the natural orbitals. We illustrate its effectiveness for molecular energy curves and chains of many atoms. We discuss the promise and challenges for realistic quantum chemical calculations.

physics.chem-ph↗

arXiv2017

Stripe order in the underdoped region of the two-dimensional Hubbard model

Competing inhomogeneous orders are a central feature of correlated electron materials including the high-temperature superconductors. The two- dimensional Hubbard model serves as the canonical microscopic physical model for such systems. Multiple orders have been proposed in the underdoped part of the phase diagram, which corresponds to a regime of maximum numerical difficulty. By combining the latest numerical methods in exhaustive simulations, we uncover the ordering in the underdoped ground state. We find a stripe order that has a highly compressible wavelength on an energy scale of a few Kelvin, with wavelength fluctuations coupled to pairing order. The favored filled stripe order is different from that seen in real materials. Our results demonstrate the power of modern numerical methods to solve microscopic models even in challenging settings.

cond-mat.str-el↗

arXiv2017

Towards the solution of the many-electron problem in real materials: equation of state of the hydrogen chain with state-of-the-art many-body methods

We present numerical results for the equation of state of an infinite chain of hydrogen atoms. A variety of modern many-body methods are employed, with exhaustive cross-checks and validation. Approaches for reaching the continuous space limit and the thermodynamic limit are investigated, proposed, and tested. The detailed comparisons provide a benchmark for assessing the current state of the art in many-body computation, and for the development of new methods. The ground-state energy per atom in the linear chain is accurately determined versus bondlength, with a confidence bound given on all uncertainties.

physics.comp-ph↗

arXiv2017

Hybrid grid/basis set discretizations of the Schrödinger equation

We present a new kind of basis function for discretizing the Schrödinger equation in electronic structure calculations, called a gausslet, which has wavelet-like features but is composed of a sum of Gaussians. Gausslets are placed on a grid and combine advantages of both grid and basis set approaches. They are orthogonal, infinitely smooth, symmetric, polynomially complete, and with a high degree of locality. Because they are formed from Gaussians, they are easily combined with traditional atom-centered Gaussian bases. We also introduce diagonal approximations which dramatically reduce the computational scaling of two-electron Coulomb terms in the Hamiltonian.

physics.chem-ph↗

arXiv2017

Disorder-Induced Mimicry of a Spin Liquid in YbMgGaO$_4$

We suggest that a randomization of the pseudo-dipolar interaction in the spin-orbit-generated low-energy Hamiltonian of YbMgGaO$_4$ due to an inhomogeneous charge environment from a natural mixing of Mg$^{2+}$ and Ga$^{3+}$ can give rise to orientational spin disorder and mimic a spin-liquid-like state. In the absence of such quenched disorder, $1/S$ and density matrix renormalization group calculations both show robust ordered states for the physically relevant phases of the model. Our scenario is consistent with the available experimental data and further experiments are proposed to support it.

cond-mat.str-el↗

arXiv2017

Matrix product state techniques for two-dimensional systems at finite temperature

The density matrix renormalization group is one of the most powerful numerical methods for computing ground-state properties of two-dimensional (2D) quantum lattice systems. Here we show its finite-temperature extensions are also viable for 2D, using the following strategy: At high temperatures, we combine density-matrix purification and numerical linked-cluster expansions to extract static observables directly in the thermodynamic limit. At low temperatures inaccessible to purification, we use the minimally entangled typical thermal state (METTS) algorithm on cylinders. We consider the triangular Heisenberg antiferromagnet as a first application, finding excellent agreement with other state of the art methods. In addition, we present a METTS-based approach that successfully extracts critical temperatures, and apply it to a frustrated lattice model. On a technical level, we compare two different schemes for performing imaginary-time evolution of 2D clusters, finding that a Suzuki-Trotter decomposition with swap gates is currently the most accurate and efficient.

cond-mat.str-el↗

arXiv2017

Sliced Basis Density Matrix Renormalization Group for Electronic Structure

We introduce a hybrid approach to applying the density matrix renormalization group (DMRG) to continuous systems, combining a grid approximation along one direction with a finite Gaussian basis set along the remaining two directions. This approach is especially useful for chain-like molecules, where the grid is used in the long direction, and we demonstrate the approach with results for hydrogen chains. The computational time for this system scales approximately linearly with the length of the chain, as we demonstrate with minimal basis set calculations with up to 1000 atoms, which are near-exact within the basis. The linear scaling comes from the combination of localization of the basis and a compression method with controlled accuracy for the long-ranged Coulomb terms in the Hamiltonian.

physics.chem-ph↗

arXiv2016

Pure density functional for strong correlations and the thermodynamic limit from machine learning

We use density-matrix renormalization group, applied to a one-dimensional model of continuum Hamiltonians, to accurately solve chains of hydrogen atoms of various separations and numbers of atoms. We train and test a machine-learned approximation to $F[n]$, the universal part of the electronic density functional, to within quantum chemical accuracy. Our calculation (a) bypasses the standard Kohn-Sham approach, avoiding the need to find orbitals, (b) includes the strong correlation of highly-stretched bonds without any specific difficulty (unlike all standard DFT approximations) and (c) is so accurate that it can be used to find the energy in the thermodynamic limit to quantum chemical accuracy.

cond-mat.str-el↗

arXiv2016

Electronic quasiparticles in the quantum dimer model: density matrix renormalization group results

We study a recently proposed quantum dimer model for the pseudogap metal state of the cuprates. The model contains bosonic dimers, representing a spin-singlet valence bond between a pair of electrons, and fermionic dimers, representing a quasiparticle with spin-$1/2$ and charge $+e$. By density matrix renormalization group calculations on a long but finite cylinder, we obtain the ground-state density distribution of the fermionic dimers for a number of different total densities. From the Friedel oscillations at open boundaries, we deduce that the Fermi surface consists of small hole pockets near $(π/2, π/2)$, and this feature persists up to a doping density of $1/16$. We also compute the entanglement entropy and find that it closely matches the sum of the entanglement entropies of a critical boson and a low density of free fermions. Our results support the existence of a fractionalized Fermi liquid in this model.

cond-mat.str-el↗

arXiv2016

Matrix Product Operators, Matrix Product States, and ab initio Density Matrix Renormalization Group algorithms

Current descriptions of the ab initio DMRG algorithm use two superficially different languages: an older language of the renormalization group and renormalized operators, and a more recent language of matrix product states and matrix product operators. The same algorithm can appear dramatically different when written in the two different vocabularies. In this work, we carefully describe the translation between the two languages in several contexts. First, we describe how to efficiently implement the ab-initio DMRG sweep using a matrix product operator based code, and the equivalence to the original renormalized operator implementation. Next we describe how to implement the general matrix product operator/matrix product state algebra within a pure renormalized operator-based DMRG code. Finally, we discuss two improvements of the ab initio DMRG sweep algorithm motivated by matrix product operator language: Hamiltonian compression, and a sum over operators representation that allows for perfect computational parallelism. The connections and correspondences described here serve to link the future developments with the past, and are important in the efficient implementation of continuing advances in ab initio DMRG and related algorithms.

physics.chem-ph↗